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Linear equations are fundamental in algebra and help us make predictions about future events based on trends. In this exercise, you encountered linear equations representing the percentage of internet users over time. A linear equation typically has the form:

• \(y = mx + b\)

where \(m\) is the slope, representing the change per year, and \(b\) is the y-intercept, representing the starting value when \(x = 0\).
In this case:

• For females, the function was \(y_1 = 5.3x + 39.5\).
• For males, the function was \(y_2 = 4.5x + 45.5\).

These equations help us understand how percentages change as years progress, where \(x\) denotes years since 2000, and \(y\) represents percentage use. Understanding these functions prepares us to solve real-world problems involving predictions.

To determine when two trends meet, such as the internet use of females and males, follow structured problem-solving steps. These steps make complex questions manageable. In our exercise, we used the following approach:

• **Identify the Equations:** Clearly write down the equations to ensure understanding. Knowing which variables and constants you are working with is essential.


• **Set Equations Equal:** Since we want to find when both percentages are equal, setting the equations equal to each other helps locate their intersection point.


• **Solve for Unknown:** After setting equations equal, solve for the unknown variable \(x\). This process involves simplifying the equation through basic algebraic operations. Once \(x\) is found, interpret what it means for your specific problem.

By following these steps, you systematically find when the percentages for females and males using the internet converge.

Solving equations, particularly linear equations, involves various algebraic techniques. These techniques simplify and make solving manageable, as shown in finding when female and male internet usage equalizes.In our solution, we used key methods, including:- **Combining Like Terms:** When faced with the equation \(5.3x + 39.5 = 4.5x + 45.5\), combine like terms by moving terms with \(x\) to one side and constants to the other. Subtract \(4.5x\) from both sides and adjust constants to simplify the equation to: \(0.8x + 39.5 = 45.5\).
- **Isolating the Variable:** After simplifying, isolate \(x\) by getting rid of constants using subtraction and division. Subtract 39.5 from both sides and divide by 0.8, leading to the solution \(x = 7.5\).
These steps show the power of basic algebraic manipulation in addressing varied mathematical situations, emphasizing neat and systematic solutions.